What other operations are there for univariate polynomials? A list of the operations is given by show(C,operations);

>

a:=C&lsqb;Random&rsqb;&ApplyFunction;

a:=−9487&plus;2831&InvisibleTimes;x−25&InvisibleTimes;x2

(2.4)

Every Domains domain has a Random function which returns a randomly generated element from a domain, which is useful for writing documentation examples! Domains can also compute with matrices and other objects. Let's compute the inverse of a 3 by 3 Hilbert matrix using Domains. First, we must create the matrix domain.

Let's now compute with matrices of polynomials in Q[x]. Let's use 2 by 2 matrices to keep the examples small.

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M:=SquareMatrix&ApplyFunction;2&comma;C&colon;

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A&coloneq;MInputx&comma;x2&comma;1−x2&comma;1&plus;x2

A:=x&comma;x2&comma;1−x2&comma;1&plus;x2

(2.8)

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MDetA&num;Compute det(A)

x−x2&plus;x3&plus;x4

(2.9)

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MInvA&num;Compute A−1

Error, (in Domains:-notImplemented) operation is not implemented

That's right, you can't compute the inverse of a matrix of polynomials, because the result is in general a rational function. Now let us demonstrate the power of Domains by doing the same Matrix problems with a Matrix of different entries, this time algebraic numbers. For example, suppose we want to compute with the roots of the polynomial m&equals;x4−10x2&plus;1. In Maple one uses the RootOf function as follows

Lazy univariate power series are "lazy" which means coefficients are computed on demand; that is, we can compute a series to higher order without having to recompute any previously computed coefficients.

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